Problem: Solve for $x$ and $y$ using elimination. ${-3x+4y = 37}$ ${3x-3y = -27}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+4y = 37}\thinspace$ to find $x$ ${-3x + 4}{(10)}{= 37}$ $-3x+40 = 37$ $-3x+40{-40} = 37{-40}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {3x-3y = -27}\thinspace$ and get the same answer for $x$ : ${3x - 3}{(10)}{= -27}$ ${x = 1}$